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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 161, Pages 65–103 (Mi into434)  

Coefficients of exponential series for analytic functions and the Pommiez operator

S. N. Melikhovab

a Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

Abstract: In this paper, we present results of the existence of a linear continuous right inverse operator for the operator of the representation of analytic functions in a bounded convex domain of the complex plane by series of quasi-polynomials and exponents. We also present closely related results on the A. F. Leontiev interpolating function and, more generally, on the the interpolating functional and the corresponding Pommiez operator. We examine cyclic vectors and closed invariant subspaces of the Pommiez operator in weighted spaces of entire functions.

Keywords: exponential series, analytic function, interpolating functional, Pommiez operator, weighted space of entire functions, cyclic vector, invariant subspace

Full text: PDF file (567 kB)
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Bibliographic databases:
UDC: 517.9
MSC: 30B50, 47B37, 47B38, 47A15, 47A16

Citation: S. N. Melikhov, “Coefficients of exponential series for analytic functions and the Pommiez operator”, Complex Analysis. Entire Functions and Their Applications, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 161, VINITI, Moscow, 2019, 65–103

Citation in format AMSBIB
\Bibitem{Mel19}
\by S.~N.~Melikhov
\paper Coefficients of exponential series for analytic functions and the Pommiez operator
\inbook Complex Analysis. Entire Functions and Their Applications
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 161
\pages 65--103
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into434}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3975491}


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